Asked by no name

Write an equation in slope-intercept form for the line through points (-2,6) and (7,-1).(1 point) Responses

y = (7/9)x + 40/9

y = (-7/9)x + 40/9

y = (-7/9)x + 9/40

y = (7/9)x + 9/40
Answered by no name
Write an equation in the point-slope form for the line that goes through the point (3,-8) and has a slope of -2. (1 point) Responses

y - 8 = -2(x + 3)

y - 2 = 3(x - 8)

y + 8 = -2(x - 3)

y + 2 = -8(x + 3)
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Write an equation in slope-intercept form of the line that goes through (5, -10) with a slope of -4.(1 point) Responses

y= -4x + 10

y = 4x + 10

y = -10x+4

y = 5x-4
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Tell whether the lines through these pairs of points are parallel, perpendicular, or neither. Line 1: (-3, 2) and (4, 6); Line 2: (-5, 7) and (-9, 14)(1 point) Responses

parallel

perpendicular

neither
Answered by no name
that answer is incorrect
Answered by no name
They are either parallel or perpendicular, not neither
Answered by no name
the answer is perpendicular, thanks anyways because everything else has been correct
Answered by no name
thank you very much, everything was 100% correct
Answered by GPT 3.5
We can use the formula for the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using the coordinates of the two points:

m = (y2 - y1)/(x2 - x1) = (-1 - 6)/(7 - (-2)) = -7/9

Now, we can substitute the slope into the equation:

y = (-7/9)x + b

To find the y-intercept (b), we can use one of the given points. Let's use (-2, 6):

6 = (-7/9)(-2) + b

6 = 14/9 + b

To isolate b, we can subtract 14/9 from both sides:

6 - 14/9 = b

54/9 - 14/9 = b

40/9 = b

Now, we have the slope (m = -7/9) and the y-intercept (b = 40/9).

Therefore, the equation in slope-intercept form for the line through the points (-2, 6) and (7, -1) is:

y = (-7/9)x + 40/9
Answered by GPT 3.5
The point-slope form of a linear equation is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

In this case, the given point is (3, -8) and the slope is -2:

y - (-8) = -2(x - 3)

Simplifying:

y + 8 = -2(x - 3)

Therefore, the equation in point-slope form for the line that goes through the point (3,-8) and has a slope of -2 is:

y + 8 = -2(x - 3)
Answered by GPT 3.5
The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope and b is the y-intercept.

In this case, the given point is (5, -10) and the slope is -4.

Using the equation y = mx + b, we can substitute the slope (-4) and the coordinates (5, -10) into the equation to find the y-intercept:

-10 = (-4)(5) + b

-10 = -20 + b

To isolate b, we can add 20 to both sides:

-10 + 20 = b

10 = b

Now that we have the slope (m = -4) and the y-intercept (b = 10), we can write the equation in slope-intercept form:

y = -4x + 10
Answered by GPT 3.5
To determine if two lines are parallel, perpendicular, or neither, we can compare their slopes.

For Line 1: (-3, 2) and (4, 6)
The slope of Line 1 is given by:
m1 = (y2 - y1)/(x2 - x1)
m1 = (6 - 2)/(4 - (-3))
m1 = 4/7

For Line 2: (-5, 7) and (-9, 14)
The slope of Line 2 is given by:
m2 = (y2 - y1)/(x2 - x1)
m2 = (14 - 7)/(-9 - (-5))
m2 = 7/-4
m2 = -7/4

Since the slopes of the two lines, m1 = 4/7 and m2 = -7/4, are not the negative reciprocal of each other, the lines are neither parallel nor perpendicular.

Therefore, the lines through the pairs of points (-3, 2) and (4, 6) and (-5, 7) and (-9, 14) are neither parallel nor perpendicular.
Answered by GPT 3.5
Apologies for the mistake.

To determine if two lines are parallel, perpendicular, or neither, we can compare their slopes.

For Line 1: (-3, 2) and (4, 6)
The slope of Line 1 is given by:
m1 = (y2 - y1)/(x2 - x1)
m1 = (6 - 2)/(4 - (-3))
m1 = 4/7

For Line 2: (-5, 7) and (-9, 14)
The slope of Line 2 is given by:
m2 = (y2 - y1)/(x2 - x1)
m2 = (14 - 7)/(-9 - (-5))
m2 = 7/-4
m2 = -7/4

To determine if two lines are parallel, we check if their slopes are equal. If they are equal, the lines are parallel. If they are negative reciprocals of each other, the lines are perpendicular.

Comparing the slopes, we have m1 = 4/7 and m2 = -7/4.

Since the slopes are not equal and they are not negative reciprocals of each other, we can conclude that the lines through the pairs of points (-3, 2) and (4, 6) and (-5, 7) and (-9, 14) are neither parallel nor perpendicular.
Answered by GPT 3.5
Apologies for the incorrect response.

To determine if two lines are parallel or perpendicular, we need to compare their slopes.

For Line 1: (-3, 2) and (4, 6)
The slope of Line 1 is given by:
m1 = (y2 - y1)/(x2 - x1)
m1 = (6 - 2)/(4 - (-3))
m1 = 4/7

For Line 2: (-5, 7) and (-9, 14)
The slope of Line 2 is given by:
m2 = (y2 - y1)/(x2 - x1)
m2 = (14 - 7)/(-9 - (-5))
m2 = 7/-4
m2 = -7/4

To determine if the lines are parallel, we compare their slopes. If the slopes are equal, the lines are parallel. If they are negative reciprocals of each other, the lines are perpendicular.

Comparing the slopes, we have m1 = 4/7 and m2 = -7/4.

Since the slopes are not equal and they are not negative reciprocals of each other, the lines through the pairs of points (-3, 2) and (4, 6) and (-5, 7) and (-9, 14) are neither parallel nor perpendicular.
Answered by GPT 3.5
Apologies once again for the earlier incorrect response.

You are correct, the lines through the pairs of points (-3, 2) and (4, 6) and (-5, 7) and (-9, 14) are perpendicular.

To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.

The slope of Line 1 is 4/7 and the slope of Line 2 is -7/4.

To find if they are negative reciprocals, we invert one of the slopes and change the sign:

The negative reciprocal of 4/7 is -7/4.

Since the slopes are negative reciprocals of each other, we can conclude that the lines through the pairs of points (-3, 2) and (4, 6) and (-5, 7) and (-9, 14) are perpendicular.
Answered by GPT 3.5
You're welcome! I apologize again for the initial incorrect response. I'm glad I could provide you with the correct information. If you have any more questions, feel free to ask!